Subgroups — #13029132

Order 1280.

798 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617116	C₂	1	1	yes	maximal, characteristic
2	#10617116	C₂	1	1	yes	maximal, characteristic
3	#10610280	C₂	1	1	yes	maximal, characteristic
4	#10604737	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604736	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#704	C₂	1	1	yes	maximal, characteristic, complemented
8	#10603864	C₂	1	1	yes	maximal, characteristic, complemented
9	#10603863	C₂	1	1	yes	maximal, characteristic, complemented
10	#10603861	C₂	1	1	yes	maximal, characteristic, complemented
11	#10603861	C₂	1	1	yes	maximal, characteristic, complemented
12	#10603811	C₂	1	1	yes	maximal, characteristic, complemented
13	#10603810	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#700	C₂	1	1	yes	maximal, characteristic, complemented
15	#10603806	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4053	C₄	1	1	yes	characteristic
17	C₂×#4047	C₄	1	1	yes	characteristic
18	#65856	C₂²	1	1	yes	characteristic
19	#65754	C₂²	1	1	yes	characteristic
20	#65754	C₂²	1	1	yes	characteristic
21	C₄×#704	C₂²	1	1	yes	characteristic
22	C₄×#704	C₂²	1	1	yes	characteristic
23	#65707	C₄	1	2	yes	—
24	#65707	C₄	1	2	yes	—
25	#65704	C₄	1	2	yes	—
26	#65704	C₄	1	2	yes	—
27	#65695	C₄	1	2	yes	—
28	#65695	C₄	1	2	yes	—
29	#65694	C₄	1	2	yes	—
30	#65694	C₄	1	2	yes	—
31	#65680	C₂²	1	1	yes	characteristic
32	#65680	C₂²	1	1	yes	characteristic
33	#65678	C₂²	1	1	yes	characteristic
34	#65678	C₂²	1	1	yes	characteristic
35	C₄×#700	C₂²	1	1	yes	characteristic
36	C₄×#700	C₂²	1	1	yes	characteristic
37	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×#405	C₄	1	1	yes	characteristic
40	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
41	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
42	#65286	C₄	1	1	yes	characteristic
43	#64997	C₄	1	1	yes	characteristic
44	#64997	C₄	1	1	yes	characteristic
45	#64996	C₂²	1	1	yes	characteristic
46	#64996	C₂²	1	1	yes	characteristic
47	#64978	C₄	1	1	yes	characteristic
48	#64978	C₄	1	1	yes	characteristic
49	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
51	#170⋊C₈	C₂²	1	1	yes	characteristic
52	#170⋊C₈	C₂²	1	1	yes	characteristic
53	#170⋊C₈	C₂²	1	1	yes	characteristic
54	#170⋊C₈	C₂²	1	1	yes	characteristic
55	#170⋊C₈	C₂²	1	1	yes	characteristic
56	#170⋊C₈	C₂²	1	1	yes	characteristic
57	#170⋊C₈	C₂²	1	1	yes	characteristic
58	#170⋊C₈	C₂²	1	1	yes	characteristic
59	#64879	C₂²	1	1	yes	characteristic
60	#64879	C₂²	1	1	yes	characteristic
61	#64879	C₂²	1	1	yes	characteristic
62	#64879	C₂²	1	1	yes	characteristic
63	C₈×#170	C₂²	1	1	yes	characteristic
64	C₈×#170	C₂²	1	1	yes	characteristic
65	C₈×#170	C₂²	1	1	yes	characteristic
66	C₈×#170	C₂²	1	1	yes	characteristic
67	#17337	—	5	1	no	maximal, Sylow
68	C₂×#709	C₂×C₄	1	1	yes	characteristic
69	C₂×#704	C₂×C₄	1	2	yes	—
70	C₂×#704	C₂×C₄	1	2	yes	—
71	C₂×#700	C₂×C₄	1	2	yes	—
72	C₂×#700	C₂×C₄	1	2	yes	—
73	C₂×D₅⋊C₈	C₂×C₄	1	2	yes	—
74	C₂×D₅⋊C₈	C₂×C₄	1	2	yes	—
75	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₅×#117	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
79	C₂×#681	C₂×C₄	1	1	yes	characteristic
80	C₂²×#168	C₂×C₄	1	1	yes	characteristic
81	#4053	—	2	4	no	—
82	#4047	—	2	4	no	—
83	C₂×#676	C₂×C₄	1	1	yes	characteristic
84	C₂×#676	C₂×C₄	1	1	yes	characteristic
85	C₂×#676	C₂×C₄	1	1	yes	characteristic
86	C₂×#676	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
90	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
91	#4039	C₂×C₄	1	1	yes	characteristic
92	#4039	C₂×C₄	1	1	yes	characteristic
93	#4033	C₂×C₄	1	1	yes	characteristic
94	#4033	C₂×C₄	1	1	yes	characteristic
95	#4027	C₂×C₄	1	1	yes	characteristic
96	#4027	C₂×C₄	1	1	yes	characteristic
97	#4027	C₂×C₄	1	1	yes	characteristic
98	#4027	C₂×C₄	1	1	yes	characteristic
99	#4018	C₂×C₄	1	1	yes	characteristic
100	#4018	C₂×C₄	1	1	yes	characteristic
101	C₄²×D₅	C₂³	1	1	yes	characteristic
102	C₄²×D₅	C₂³	1	1	yes	characteristic
103	C₂²⋊#170	C₂×C₄	1	2	yes	—
104	C₂²⋊#170	C₂×C₄	1	2	yes	—
105	#4004	C₂×C₄	1	2	yes	—
106	#4004	C₂×C₄	1	2	yes	—
107	#4004	C₂×C₄	1	2	yes	—
108	#4004	C₂×C₄	1	2	yes	—
109	#4003	C₂×C₄	1	2	yes	—
110	#4003	C₂×C₄	1	2	yes	—
111	#4003	C₂×C₄	1	2	yes	—
112	#4003	C₂×C₄	1	2	yes	—
113	#4002	C₂×C₄	1	2	yes	—
114	#4002	C₂×C₄	1	2	yes	—
115	#4002	C₂×C₄	1	2	yes	—
116	#4002	C₂×C₄	1	2	yes	—
117	C₄⋊#170	C₂×C₄	1	2	yes	—
118	C₄⋊#170	C₂×C₄	1	2	yes	—
119	C₄×#170	C₂×C₄	1	2	yes	—
120	C₄×#170	C₂×C₄	1	2	yes	—
121	C₄×#170	C₂³	1	1	yes	characteristic
122	C₄×#170	C₂³	1	1	yes	characteristic
123	C₄×#170	C₂³	1	1	yes	characteristic
124	C₄×#170	C₂³	1	1	yes	characteristic
125	C₄×#170	C₂³	1	1	yes	characteristic
126	C₄×#170	C₂³	1	1	yes	characteristic
127	C₄×#170	C₂³	1	1	yes	characteristic
128	C₄×#170	C₂³	1	1	yes	characteristic
129	C₅×#97	C₂×C₄	1	1	yes	characteristic
130	C₅×#97	C₂×C₄	1	1	yes	characteristic
131	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
132	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
133	#3947	C₂×C₄	1	1	yes	characteristic
134	#3947	C₂×C₄	1	1	yes	characteristic
135	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
137	C₈×Dic₅	C₂³	1	1	yes	characteristic
138	C₈×Dic₅	C₂³	1	1	yes	characteristic
139	C₈×Dic₅	C₂³	1	1	yes	characteristic
140	C₈×Dic₅	C₂³	1	1	yes	characteristic
141	#3935	C₂×C₄	1	1	yes	characteristic
142	#3935	C₂×C₄	1	1	yes	characteristic
143	C₄×#168	C₂×C₄	1	1	yes	characteristic
144	C₄×#168	C₂×C₄	1	1	yes	characteristic
145	#2965	—	5	1	no	—
146	#2965	—	5	1	no	—
147	C₄×#131	—	5	1	no	—
148	#1455	—	5	1	no	—
149	#1455	—	5	1	no	—
150	#1453	—	5	1	no	—
151	#1453	—	5	1	no	—
152	#1452	—	5	1	no	—
153	#1451	—	5	1	no	—
154	#1451	—	5	1	no	—
155	C₈×M₁₆	—	5	1	no	—
156	C₈×M₁₆	—	5	1	no	—
157	C₈×M₁₆	—	5	1	no	—
158	C₈×M₁₆	—	5	1	no	—
159	C₂×#322	—	5	1	no	—
160	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
162	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
163	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
165	#709	—	2	2	no	—
166	#709	—	2	2	no	—
167	C₂×D₂₀	C₄²	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
175	#704	—	2	4	no	—
176	#704	—	4	2	no	—
177	C₂×#170	C₂²×C₄	1	2	yes	—
178	C₂×#170	C₂²×C₄	1	2	yes	—
179	C₂×#170	C₂²×C₄	1	2	yes	—
180	C₂×#170	C₂²×C₄	1	2	yes	—
181	C₂×#170	C₂²×C₄	1	2	yes	—
182	C₂×#170	C₂²×C₄	1	2	yes	—
183	C₂×#170	C₂²×C₄	1	2	yes	—
184	C₂×#170	C₂²×C₄	1	2	yes	—
185	#700	—	2	4	no	—
186	#700	—	4	2	no	—
187	D₅⋊C₈	—	2	4	no	—
188	D₅⋊C₈	—	4	2	no	—
189	C₅×M₁₆	—	2	2	no	—
190	C₂×C₅×C₈	—	2	2	no	—
191	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
197	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
198	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
199	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
201	#685	C₄²	1	1	yes	characteristic
202	#685	C₄²	1	1	yes	characteristic
203	#685	C₄²	1	1	yes	characteristic
204	#685	C₄²	1	1	yes	characteristic
205	#683	C₄²	1	1	yes	characteristic
206	#683	C₄²	1	1	yes	characteristic
207	#683	C₄²	1	1	yes	characteristic
208	#683	C₄²	1	1	yes	characteristic
209	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
210	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
211	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
212	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
214	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
215	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
217	#681	—	2	2	no	—
218	C₂×#168	—	2	2	no	—
219	C₂×#168	C₂²×C₄	1	1	yes	characteristic
220	C₂×#168	C₂²×C₄	1	1	yes	characteristic
221	C₂×#168	C₂²×C₄	1	1	yes	characteristic
222	C₂×#168	C₂²×C₄	1	1	yes	characteristic
223	#676	—	2	2	no	—
224	#676	—	2	2	no	—
225	#676	M₁₆	1	4	yes	complemented
226	#676	M₁₆	1	4	yes	complemented
227	C₈×D₅	—	2	2	no	—
228	C₈×D₅	—	2	2	no	—
229	C₈×D₅	—	2	2	no	—
230	C₈×D₅	—	2	2	no	—
231	C₂×#131	—	5	1	no	—
232	C₂×#131	—	5	1	no	—
233	C₄×#41	—	5	1	no	—
234	#446	—	5	2	no	—
235	#446	—	5	2	no	—
236	#436	—	5	2	no	—
237	#436	—	5	2	no	—
238	#435	—	5	2	no	—
239	#435	—	5	2	no	—
240	#435	—	5	2	no	—
241	#435	—	5	2	no	—
242	#431	—	5	1	no	—
243	#431	—	5	1	no	—
244	#431	—	5	1	no	—
245	#431	—	5	1	no	—
246	#431	—	5	1	no	—
247	#431	—	5	1	no	—
248	#405	—	5	1	no	—
249	#405	—	5	1	no	—
250	#405	—	5	1	no	—
251	#405	—	5	1	no	—
252	#405	—	5	1	no	—
253	#405	AGL(1,𝔽₅)	1	1	yes	characteristic
254	C₄×M₁₆	—	5	1	no	—
255	C₄×M₁₆	—	5	1	no	—
256	C₄×M₁₆	—	5	1	no	—
257	C₄×M₁₆	—	5	1	no	—
258	C₄×M₁₆	—	5	1	no	—
259	C₄×M₁₆	—	5	1	no	—
260	C₄×M₁₆	—	5	1	no	—
261	C₂×C₄×C₈	—	5	1	no	—
262	C₂×C₄×C₈	—	5	1	no	—
263	C₂×C₄×C₈	—	5	1	no	—
264	C₂×C₄×C₈	—	5	1	no	—
265	C₂×C₄×C₈	—	5	1	no	—
266	#322	—	5	1	no	—
267	#322	—	5	1	no	—
268	#322	—	5	1	no	—
269	#322	—	5	1	no	—
270	#322	—	5	1	no	—
271	#322	—	5	1	no	—
272	#322	—	5	1	no	—
273	#322	—	5	1	no	—
274	#322	—	5	1	no	—
275	#322	—	5	1	no	—
276	#322	—	5	1	no	—
277	#322	—	5	1	no	—
278	C₈²	—	5	1	no	—
279	C₈²	—	5	1	no	—
280	C₈²	—	5	1	no	—
281	C₈²	—	5	1	no	—
282	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
283	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
284	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
293	C₂²⋊D₅	—	2	2	no	—
294	C₂²⋊D₅	—	2	2	no	—
295	C₂×Dic₅	—	2	2	no	—
296	C₂×Dic₅	—	2	2	no	—
297	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
298	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
299	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
300	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
301	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
302	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
303	D₂₀	—	2	2	no	—
304	C₄×D₅	—	2	1	no	—
305	C₄×D₅	—	2	1	no	—
306	C₄×D₅	—	2	2	no	—
307	C₄×D₅	—	2	2	no	—
308	C₄×D₅	—	2	2	no	—
309	C₄×D₅	—	2	2	no	—
310	C₄×D₅	C₂×M₁₆	1	2	yes	—
311	C₄×D₅	C₂×M₁₆	1	2	yes	—
312	Dic₁₀	—	2	2	no	—
313	#170	—	2	2	no	—
314	#170	—	2	2	no	—
315	#170	—	2	2	no	—
316	#170	—	2	2	no	—
317	#170	—	2	2	no	—
318	#170	—	2	2	no	—
319	#170	—	2	2	no	—
320	#170	#131	1	4	yes	complemented
321	C₅×C₈	—	2	1	no	—
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	C₂×M₁₆	1	2	yes	—
324	C₅×C₈	C₂×M₁₆	1	2	yes	—
325	#168	—	2	1	no	—
326	#168	—	2	1	no	—
327	#168	C₂×M₁₆	1	2	yes	—
328	#168	C₂×M₁₆	1	2	yes	—
329	C₂×#41	—	5	1	no	—
330	#131	—	10	4	no	—
331	#131	—	10	4	no	—
332	C₂×M₁₆	—	5	2	no	—
333	C₂×M₁₆	—	5	2	no	—
334	C₂×M₁₆	—	5	1	no	—
335	C₂×M₁₆	—	5	2	no	—
336	C₂×M₁₆	—	5	2	no	—
337	C₂×M₁₆	—	5	1	no	—
338	C₂×M₁₆	—	5	1	no	—
339	C₂×M₁₆	—	5	1	no	—
340	C₂×M₁₆	—	5	1	no	—
341	C₂×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
342	C₂²×C₈	—	5	2	no	—
343	C₂²×C₈	—	5	1	no	—
344	C₂²×C₈	—	5	2	no	—
345	C₂²×C₈	—	5	1	no	—
346	C₂²×C₈	—	5	1	no	—
347	C₂²×C₈	—	5	1	no	—
348	C₂²×C₈	—	5	1	no	—
349	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₄×Q₈	—	5	1	no	—
351	C₄×Q₈	—	5	1	no	—
352	C₄×D₄	—	5	1	no	—
353	C₄×D₄	—	5	1	no	—
354	C₄×D₄	—	5	1	no	—
355	C₄×D₄	—	5	1	no	—
356	C₄×D₄	—	5	1	no	—
357	C₄×D₄	—	5	1	no	—
358	#117	—	5	1	no	—
359	#117	—	5	1	no	—
360	#117	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₂×C₄²	—	5	1	no	—
362	C₂×C₄²	—	5	1	no	—
363	C₂×C₄²	—	5	1	no	—
364	C₄⋊C₈	—	5	2	no	—
365	C₄⋊C₈	—	5	2	no	—
366	C₄⋊C₈	—	5	2	no	—
367	C₄⋊C₈	—	5	2	no	—
368	C₄⋊C₈	—	5	2	no	—
369	C₄⋊C₈	—	5	2	no	—
370	C₂²⋊C₈	—	5	2	no	—
371	C₂²⋊C₈	—	5	2	no	—
372	C₂²⋊C₈	—	5	2	no	—
373	C₂²⋊C₈	—	5	2	no	—
374	C₂²⋊C₈	—	5	2	no	—
375	C₂²⋊C₈	—	5	2	no	—
376	#97	—	5	2	no	—
377	#97	—	5	2	no	—
378	#97	—	5	2	no	—
379	#97	—	5	2	no	—
380	#97	—	5	1	no	—
381	#97	—	5	1	no	—
382	#97	—	5	1	no	—
383	#97	—	5	1	no	—
384	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
385	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₄×C₈	—	5	1	no	—
387	C₄×C₈	—	5	1	no	—
388	C₄×C₈	—	5	1	no	—
389	C₄×C₈	—	5	1	no	—
390	C₄×C₈	—	5	1	no	—
391	C₄×C₈	—	5	1	no	—
392	C₄×C₈	—	5	1	no	—
393	C₄×C₈	—	5	1	no	—
394	C₄×C₈	—	5	2	no	—
395	C₄×C₈	—	5	2	no	—
396	C₄×C₈	—	5	1	no	—
397	C₄×C₈	—	5	1	no	—
398	C₄×C₈	—	5	1	no	—
399	C₄×C₈	—	5	1	no	—
400	C₄×C₈	—	5	1	no	—
401	C₄×C₈	—	5	1	no	—
402	C₄×C₈	—	5	1	no	—
403	C₄×C₈	—	5	1	no	—
404	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
405	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	2	1	no	—
408	C₂²×C₅	—	2	1	no	—
409	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
410	C₂×D₅	—	2	1	no	—
411	C₂×D₅	—	2	1	no	—
412	C₂×D₅	—	2	1	no	—
413	C₂×D₅	—	2	1	no	—
414	C₂×D₅	—	2	1	no	—
415	C₂×D₅	C₄×M₁₆	1	2	yes	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
422	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
423	Dic₅	—	2	1	no	—
424	Dic₅	—	2	1	no	—
425	Dic₅	—	2	1	no	—
426	Dic₅	C₄×M₁₆	1	2	yes	—
427	Dic₅	C₂×#131	1	2	yes	—
428	Dic₅	#568	1	2	yes	—
429	#41	—	10	2	no	—
430	#41	—	10	2	no	—
431	C₂×Q₈	—	5	1	no	—
432	C₂×D₄	—	5	1	no	—
433	C₂×D₄	—	5	1	no	—
434	C₂×D₄	—	5	1	no	—
435	C₂²×C₄	—	5	1	no	—
436	C₂²×C₄	—	5	1	no	—
437	C₂²×C₄	—	5	1	no	—
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	5	1	no	—
440	C₂²×C₄	—	5	1	no	—
441	C₂²×C₄	—	5	1	no	—
442	C₂²×C₄	—	5	1	no	—
443	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
444	M₁₆	—	2	2	no	—
445	M₁₆	—	5	4	no	—
446	M₁₆	—	5	4	no	—
447	M₁₆	—	10	2	no	—
448	M₁₆	—	10	2	no	—
449	M₁₆	—	10	4	no	—
450	M₁₆	—	10	4	no	—
451	M₁₆	—	10	2	no	—
452	M₁₆	—	20	2	no	—
453	M₁₆	—	20	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	5	2	no	—
456	C₂×C₈	—	5	1	no	—
457	C₂×C₈	—	5	1	no	—
458	C₂×C₈	—	5	2	no	—
459	C₂×C₈	—	5	2	no	—
460	C₂×C₈	—	5	2	no	—
461	C₂×C₈	—	5	2	no	—
462	C₂×C₈	—	5	2	no	—
463	C₂×C₈	—	5	2	no	—
464	C₂×C₈	—	5	2	no	—
465	C₂×C₈	—	5	1	no	—
466	C₂×C₈	—	5	1	no	—
467	C₂×C₈	—	10	2	no	—
468	C₂×C₈	—	10	2	no	—
469	C₂×C₈	—	10	2	no	—
470	C₂×C₈	—	10	2	no	—
471	C₂×C₈	—	10	4	no	—
472	C₂×C₈	—	10	2	no	—
473	C₂×C₈	—	20	2	no	—
474	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
476	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
478	C₄⋊C₄	—	5	1	no	—
479	C₄⋊C₄	—	5	1	no	—
480	C₄⋊C₄	—	5	1	no	—
481	C₄⋊C₄	—	5	1	no	—
482	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
483	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
484	C₂²⋊C₄	—	5	1	no	—
485	C₂²⋊C₄	—	5	1	no	—
486	C₂²⋊C₄	—	5	1	no	—
487	C₂²⋊C₄	—	5	1	no	—
488	C₂²⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
489	C₂²⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
490	C₄²	—	5	1	no	—
491	C₄²	—	5	1	no	—
492	C₄²	—	5	1	no	—
493	C₄²	—	5	1	no	—
494	C₄²	—	5	1	no	—
495	C₄²	—	5	1	no	—
496	C₄²	—	5	1	no	—
497	C₄²	—	5	1	no	—
498	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
499	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
500	C₂×C₅	—	4	1	no	—
501	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
502	C₂×C₅	C₄×#131	1	1	yes	characteristic
503	C₂×C₅	#2875	1	1	yes	characteristic
504	D₅	—	2	2	no	—
505	D₅	—	4	1	no	—
506	C₂³	—	5	1	no	—
507	C₂³	—	5	1	no	—
508	C₂³	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
509	Q₈	—	10	2	no	—
510	D₄	—	10	2	no	—
511	D₄	—	10	2	no	—
512	D₄	—	10	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	5	1	no	—
516	C₂×C₄	—	5	1	no	—
517	C₂×C₄	—	5	1	no	—
518	C₂×C₄	—	5	2	no	—
519	C₂×C₄	—	5	2	no	—
520	C₂×C₄	—	5	1	no	—
521	C₂×C₄	—	5	1	no	—
522	C₂×C₄	—	5	1	no	—
523	C₂×C₄	—	10	2	no	—
524	C₂×C₄	—	10	2	no	—
525	C₂×C₄	—	10	2	no	—
526	C₂×C₄	—	10	2	no	—
527	C₂×C₄	—	10	2	no	—
528	C₂×C₄	—	10	2	no	—
529	C₂×C₄	—	10	1	no	—
530	C₂×C₄	—	10	1	no	—
531	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
532	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
533	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
534	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
535	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
536	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	5	4	no	—
540	C₈	—	5	2	no	—
541	C₈	—	5	2	no	—
542	C₈	—	10	2	no	—
543	C₈	—	10	2	no	—
544	C₈	—	10	2	no	—
545	C₈	—	10	2	no	—
546	C₈	—	10	2	no	—
547	C₈	—	10	2	no	—
548	C₈	—	10	2	no	—
549	C₈	—	10	1	no	—
550	C₈	—	10	1	no	—
551	C₈	D₅⋊M₁₆	1	2	yes	—
552	C₈	D₅⋊M₁₆	1	2	yes	—
553	C₅	#17337	1	1	yes	characteristic, complemented, Sylow
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	5	2	no	—
558	C₂²	—	10	1	no	—
559	C₂²	—	10	1	no	—
560	C₂²	—	10	1	no	—
561	C₂²	—	10	1	no	—
562	C₂²	—	10	1	no	—
563	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	5	2	no	—
570	C₄	—	5	2	no	—
571	C₄	—	5	2	no	—
572	C₄	—	10	1	no	—
573	C₄	—	10	1	no	—
574	C₄	—	10	1	no	—
575	C₄	C₂×D₅⋊M₁₆	1	1	yes	characteristic
576	C₄	C₂×D₅⋊M₁₆	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	—	10	2	no	—
579	C₂	—	20	1	no	—
580	C₂	C₄×D₅⋊M₁₆	1	1	yes	characteristic
581	C₂	AGL(1,𝔽₅)×#131	1	1	yes	characteristic
582	C₂	#10617415	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#405	C₄
prime radical	C₂×#709	C₂×C₄
cosocle	C₄×Dic₅	C₂⁴
hypercenter	#405	AGL(1,𝔽₅)
hypocenter	C₅	#17337
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #10604737	C₂	semidirect
5. #10604736	C₂	semidirect
6. #10604688	C₂	semidirect
7. C₈×#704	C₂	semidirect
8. #10603864	C₂	semidirect
9. #10603863	C₂	semidirect
10. #10603861	C₂	semidirect
11. #10603861	C₂	semidirect
12. #10603811	C₂	semidirect
13. #10603810	C₂	semidirect
14. C₈×#700	C₂	semidirect
15. #10603806	C₂	semidirect
225. #676	M₁₆	semidirect
226. #676	M₁₆	semidirect
320. #170	#131	semidirect
553. C₅	#17337	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10617116	2
#10610280	2
#10604737	2
#10604736	2
#10604688	2
C₈×#704	2
#10603864	2
#10603863	2
#10603861	2
#10603811	2
#10603810	2
C₈×#700	2
#10603806	2
#17337	5